[tex]\sin(3\theta)=-1\\\\subtitute\ 3\theta=\alpha\\\\therefore\\\\\sin(3\theta)=\sin\alpha=-1\iff\alpha=270^o+360^o\cdot k\ or\ equivalent\ \alpha=\frac{3}{2}\pi+2k\pi[/tex]
[tex]3\theta=270^o+360^o\cdot k\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{\theta=90^o+120^o\cdot k}\\\\equivalent\\\\3\theta=\frac{3}{2}\pi+2k\pi\ \ \ \ |divid\ both\ sides\ by\ 3\\\\\boxed{\theta=\frac{1}{2}\pi+\frac{2}{3}k\pi}[/tex]
